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1. A Framework for Simulating Multiple Contagions Over Multiple Networks

   Kishore, Aparna; Machi, Lucas; Kuhlman, Chris J.; Machi, Dustin; Ravi, S.S. (January 2021, Complex Networks and Their Applications)

   null (Ed.)

   Many contagion processes evolving on populations do so simultaneously, interacting over time. Examples are co-evolution of human social processes and diseases, such as the uptake of mask wearing and disease spreading. Commensurately, multi-contagion agent-based simulations (ABSs) that represent populations as networks in order to capture interactions between pairs of nodes are becoming more popular. In this work, we present a new ABS system that simulates any number of contagions co-evolving on any number of networked populations. Individual (interacting) contagion models and individual networks are speci ed, and the system computes multi-contagion dynamics over time. This is a signi cant improvement over simulation frameworks that require union graphs to handle multiple networks, and/or additional code to orchestrate the computations of multiple contagions. We provide a formal model for the simulation system, an overview of the software, and case studies that illustrate applications of interacting contagions. 

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2. Influence Propagation with Multiple Stages over Random Multiplex Networks

   https://doi.org/10.1109/GLOBECOM38437.2019.9013531  

   Zhuang, Yong; Yagan, Osman (December 2019, 2019 IEEE Global Communications Conference (GLOBECOM))

   Complex contagion models have been developed to understand a wide range of social phenomena such as adoption of cultural fads, the diffusion of belief, norms, and innovations in social networks, and the rise of collective action to join a riot. Most existing works focus on contagions where individuals’ states are represented by binary variables, and propagation takes place over a single isolated network. However, characterization of an individual’s standing on a given matter as a binary state might be overly simplistic as most of our opinions, feelings, and perceptions vary over more than two states. Also, most real-world contagions take place over multiple networks (e.g., Twitter and Facebook) or involve multiplex networks where individuals engage in different types of relationships (e.g., co-worker, family, etc.). To this end, this paper studies multi-stage complex contagions that take place over multi-layer or multiplex networks. Under a linear threshold based contagion model, we first give analytic results for the expected size of global cascades, i.e., cases where a randomly chosen node can initiate a propagation that eventually reaches a positive fraction of the whole population. Then, analytic results are confirmed by an extensive numerical study. In addition, we demonstrate how the dynamics of complex contagions is affected by the structural properties of the networks. In particular, we reveal an interesting connection between the assortativity of a network and the impact of hyper-active nodes on the cascade size. 

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3. Using Dominating Sets to Block Contagions in Social Networks

   Bao, R.; Hancock, M.; Kuhlman, C.; Ravi, S.S. (November 2022, IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining)

   Abstract—There are myriad real-life examples of contagion processes on human social networks, e.g., spread of viruses, information, and social unrest. Also, there are many methods to control or block contagion spread. In this work, we introduce a novel method of blocking contagions that uses nodes from dominating sets (DSs). To our knowledge, this is the first use of DS nodes to block contagions. Finding minimum dominating sets of graphs is an NP-Complete problem, so we generalize a well-known heuristic, enabling us to customize its execution. Our method produces a prioritized list of dominating nodes, which is, in turn, a prioritized list of blocking nodes. Thus, for a given network, we compute this list of blocking nodes and we use it to block contagions for all blocking node budgets, contagion seed sets, and parameter values of the contagion model. We report on computational experiments of the blocking efficacy of our approach using two mined networks. We also demonstrate the effectiveness of our approach by comparing blocking results with those from the high degree heuristic, which is a common standard in blocking studies. Index Terms—contagion blocking, dominating sets, threshold models, social networks, simulation, high degree heuristic 

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4. Blocking Social Contagions via Dominating Sets Using a Modified Integer Linear Program Formulation

   Bao, Robert C; Kuhlman, Chris J; Ravi, S S (September 2024, IEEE)

   Researchers have modeled contagion processes on social networks for wide ranging applications, including spreading of epidemics, financial defaults, actions such as joining social media sites, and rumors. So, too, researchers have developed a host of intervention methods to control harmful contagions on networks; among these approaches are node and edge removal, separating network communities, altering contagion properties, and introducing a second competing contagion. In this work, minimum dominating sets are used to identify blocking nodes—nodes that do not contract a contagion and therefore also do not assist in transmitting it. A novel, generalized method that utilizes integer linear programming to determine exact minimum dominating sets (which is an NP-hard problem) has been developed for a subgraph of any social network for any combination of covering distance and coverage requirement. Three social networks are used to understand and evaluate (i) the method itself and (ii) the efficacy of the blocking nodes that the method produces to stop contagion spread. 

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5. Diffusion in Social Networks: Effects of Monophilic Contagion, Friendship Paradox and Reactive Networks

   https://doi.org/10.1109/TNSE.2019.2909015  

   Nettasinghe, Buddhika; Krishnamurthy, Vikram; Lerman, Kristina (April 2019, IEEE Transactions on Network Science and Engineering)

   We consider SIS contagion processes over networks where, a classical assumption is that individuals' decisions to adopt a contagion are based on their immediate neighbors. However, recent literature shows that some attributes are more correlated between two-hop neighbors, a concept referred to as monophily. This motivates us to explore monophilic contagion, the case where a contagion (e.g. a product, disease) is adopted by considering two-hop neighbors instead of immediate neighbors (e.g. you ask your friend about the new iPhone and she recommends you the opinion of one of her friends). We show that the phenomenon called friendship paradox makes it easier for the monophilic contagion to spread widely. We also consider the case where the underlying network stochastically evolves in response to the state of the contagion (e.g. depending on the severity of a flu virus, people restrict their interactions with others to avoid getting infected) and show that the dynamics of such a process can be approximated by a differential equation whose trajectory satisfies an algebraic constraint restricting it to a manifold. Our results shed light on how graph theoretic consequences affect contagions and, provide simple deterministic models to approximate the collective dynamics of contagions over stochastic graph processes. 

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